Am I correct in saying that the angular deficit (change in angle) of a vector transported around a closed surface on a curved surface can only be observed by flattening the surface?(adsbygoogle = window.adsbygoogle || []).push({});

Actually a further problem- I understand it from the flat sheet to a cone: Cut out a pie from a sheet, Draw a (incomplete) circle around the tip of the pie, Draw arrows pointing in the same direction (parallel) along the circle (i.e. parallel transport on the flat surface with the pie cut out) and now roll the sheet into a cone with the pie tip as cone tip and matching the edges of the pie. The arrows are no longer parallel.

But I have not understood it starting from a cone. Now the surface is curved, what is a parallel vector, does it stay on the surface? How do I try to parallel transport a vector on the circle on a cone? Any clear examples available.

I sort of do understand the Tensor math. I am looking for a visual explanation.

**Physics Forums - The Fusion of Science and Community**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Parallel transporting of a vector in curved space

Loading...

Similar Threads - Parallel transporting vector | Date |
---|---|

A Global solution to parallel transport equation? | Nov 15, 2017 |

I Lie Derivatives vs Parallel Transport | Nov 6, 2017 |

I Parallel transport vs Fermi Transport | Jun 30, 2017 |

How do we parallel transport a vector? | Oct 19, 2013 |

Parallel transport of a vector. | Jul 14, 2011 |

**Physics Forums - The Fusion of Science and Community**